PARTIAL-DERIVATIVE-METHOD WITH NONZERO BACKGROUND POTENTIAL - APPLICATION TO INVERSE SCATTERING FOR THE 2-DIMENSIONAL ACOUSTIC EQUATION

We generalize a number of formulas of the partial derivative- method f or the Schrodinger equation to the case of nonzero background potentia l. As a corollary we have found the following reciprocity property of the Faddeev function h: h(k, l) = h(-l, -k), k, l is an element of C-n , k(2) = l(2), Im k = Iml not equal 0, where h is a non-analytic exten sion of the scattering amplitude to the complex domain. As an applicat ion we prove the uniqueness theorem and give a reconstruction procedur e in the inverse scattering problem for the two-dimensional acoustic e quation.